Lax–Sato integrable dispersionless systems on supermanifolds related to a centrally extended generalization of the loop superconformal Lie algebra

Authors

  • O. Hentosh Institute of Applied Problems of Mechanics and Mathematics named after Ya. S. Pidstryhach, NAS of Ukraine, Lviv

DOI:

https://doi.org/10.3842/umzh.v77i9.7950

Keywords:

dispersionless systems, Lax-Sato integrability, superconformal vector fields, semi-direct sum, Adler-Kostant-Symes theory, Casimir invariant

Abstract

UDC 517.9

We propose a new Lie-algebraic approach to the construction of Lax–Sato integrable dispersionless systems on functional supermanifolds by means of the centrally extended semidirect sum of the loop Lie algebra of  superconformal vector fields on a supertorus and its regular dual space, which is based on the general Adler–Kostant–Symes  Lie-algebraic scheme. By using this approach, we obtain the Lax–Sato integrable superanalogs for some systems of Mikhalev–Pavlov-type dispersionless equations  given on functional supermanifolds of four commuting and numerous anticommuting independent variables and find the left gradients of the Casimir invariant reduced to the orbits of the coadjoint action of the central extension, related to these systems, as well as the associated pairs of compatible Poisson operators.

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06.11.2025

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Vol. 77 No. 9 (2025)

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Research articles

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How to Cite

Hentosh, O. “Lax–Sato Integrable Dispersionless Systems on Supermanifolds Related to a Centrally Extended Generalization of the Loop Superconformal Lie Algebra”. Ukrains’kyi Matematychnyi Zhurnal, vol. 77, no. 9, Nov. 2025, pp. 555–572, https://doi.org/10.3842/umzh.v77i9.7950.